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Introduction to Ratios Video Lecture | CSAT Preparation - UPSC
FAQs on Introduction to Ratios Video Lecture - CSAT Preparation - UPSC
| 1. What are ratios and why are they important in mathematics? |  |
Ratios are mathematical expressions that compare two or more quantities. They are important in mathematics because they allow us to compare and analyze relationships between different amounts or values. Ratios help us understand proportions, scale factors, and rates of change, which are crucial in various real-life applications such as cooking, finance, and engineering.
| 2. How do you simplify a ratio? | |
To simplify a ratio, you need to find the greatest common divisor (GCD) of the numbers in the ratio and divide both the numerator and denominator by the GCD. This process ensures that the ratio is in its simplest form. For example, if you have a ratio of 8:12, the GCD of 8 and 12 is 4. Dividing both 8 and 12 by 4 gives the simplified ratio of 2:3.
| 3. Can ratios be expressed as fractions or decimals? | |
Yes, ratios can be expressed as fractions or decimals. In fact, ratios are often represented as fractions, where the numerator represents the first quantity being compared and the denominator represents the second quantity. For example, a ratio of 3:5 can be written as the fraction 3/5 or the decimal 0.6.
| 4. How are ratios used in financial analysis? | |
Ratios are extensively used in financial analysis to assess the performance and health of businesses. Financial ratios, such as the debt-to-equity ratio, return on investment (ROI), or the current ratio, provide valuable insights into a company's liquidity, profitability, and efficiency. By comparing these ratios over time or against industry benchmarks, investors and analysts can make informed decisions about investing in or lending to a company.
| 5. Can ratios be used to solve proportions? | |
Yes, ratios can be used to solve proportions. Proportions are equations that involve two ratios that are equal to each other. By setting up the proportion and cross-multiplying, you can solve for an unknown value. For example, if you have the proportion 2:5 = x:10, you can cross-multiply to get 2 * 10 = 5 * x, which simplifies to 20 = 5x. Solving for x gives x = 4.
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